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What is the sum of the digits of integer x, where x = 4^10* 5^13?

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What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

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New post 05 Nov 2017, 02:38
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

72% (01:16) correct 28% (01:50) wrong based on 67 sessions

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Kudos [?]: 133105 [0], given: 12410

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Kudos [?]: 24 [1], given: 105

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Re: What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

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New post 05 Nov 2017, 02:58
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X= 2^20*5^13
= 10^13 *2^7
= 128*10^13

Sum of digits = 11
Option B

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Kudos [?]: 13 [0], given: 27

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Re: What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

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New post 05 Nov 2017, 12:15
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Bunuel wrote:
What is the sum of the digits of integer x, where \(x = 4^{10} * 5^{13}\)?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5


Answer is B as follows

\(x = 4^{10} * 5^{13} = 2^{20}*5^{13} = 10^{13}*2^7 = 10^{13}*128\)
Sum of the digits = 1+2+8 = 11

Hence B
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Kudos [?]: 13 [0], given: 27

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Kudos [?]: 0 [0], given: 5

Re: What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

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New post 07 Nov 2017, 09:05
Since we are looking for the sum of the digits we can simplify this problem by removing the trailing zeros (zeros at the end of the number). Trailing zeros are added to a number when multiplied by 10.

Remember 10 = 2 * 5
Thus, in our problem 4^10*5^13 or:
2^20 * 5^13

As you can see we have the pair 2*5 thirteen times. We can remove 2^13 and 5^13 and work with the rest which is 2^7 = 128

1+2+8 = 11

Kudos [?]: 0 [0], given: 5

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Re: What is the sum of the digits of integer x, where x = 4^10* 5^13? [#permalink]

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New post 08 Nov 2017, 17:35
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Expert's post
Bunuel wrote:
What is the sum of the digits of integer x, where \(x = 4^{10} * 5^{13}\)?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5



We can simplify the given equation:

x = 4^10 x 5^13

x = 2^20 x 5^13

x = 2^7 x 2^13 x 5^13

x = 2^7 x 10^13

x = 128 x 10^13

We see that x is the number 128 followed by 13 zeros. Thus, the sum of the digits of x is 1 + 2 + 8 = 11.

Answer: B
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Kudos [?]: 914 [1], given: 5

Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?   [#permalink] 08 Nov 2017, 17:35
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